Left Termination of the query pattern at_in_2(a, a) w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

at(X, fido) :- ','(at(X, mary), near(X)).
at(ta, mary).
at(jm, mary).
near(jm).

Queries:

at(a,a).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

(2) Obligation:

Triples:


Clauses:


Afs:

(3) TPisEmptyProof (EQUIVALENT transformation)

There are no more dependency triples. Hence, the dependency triple problem trivially terminates.

(4) YES